1,680 research outputs found
On the cone eigenvalue complementarity problem for higher-order tensors
In this paper, we consider the tensor generalized eigenvalue complementarity
problem (TGEiCP), which is an interesting generalization of matrix eigenvalue
complementarity problem (EiCP). First, we given an affirmative result showing
that TGEiCP is solvable and has at least one solution under some reasonable
assumptions. Then, we introduce two optimization reformulations of TGEiCP,
thereby beneficially establishing an upper bound of cone eigenvalues of
tensors. Moreover, some new results concerning the bounds of number of
eigenvalues of TGEiCP further enrich the theory of TGEiCP. Last but not least,
an implementable projection algorithm for solving TGEiCP is also developed for
the problem under consideration. As an illustration of our theoretical results,
preliminary computational results are reported.Comment: 26 pages, 2 figures, 3 table
Homotopy Methods to Compute Equilibria in Game Theory
This paper presents a complete survey of the use of homotopy methods in game theory.Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by variousselection theories. We present all relevant techniques underlying homotopy algorithms.We give detailed expositions of the Lemke-Howson algorithm and the Van den Elzen-Talman algorithm to compute Nash equilibria in 2-person games, and the Herings-Vanden Elzen, Herings-Peeters, and McKelvey-Palfrey algorithms to compute Nash equilibriain general n-person games.operations research and management science;
Market Equilibrium in Exchange Economies with Some Families of Concave Utility Functions
We present explicit convex programs which characterize the equilibrium for certain additively separable utility functions and CES functions. These include some CES utility functions that do not satisfy weak gross substitutability.Exchange economy, computation of equilibria, convex feasibility problem
A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn--Hilliard--Navier--Stokes system
This paper is concerned with the development and implementation of an adaptive solution algorithm for the optimal control of a time-discrete Cahn--Hilliard--Navier--Stokes system with variable densities. The free energy density associated to the Cahn--Hilliard system incorporates the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the Navier--Stokes equation. A dual-weighed residual approach for goal-oriented adaptive finite elements is presented which is based on the concept of C-stationarity. The overall error representation depends on primal residual weighted by approximate dual quantities and vice versa as well as various complementary mismatch errors. Details on the numerical realization of the adaptive concept and a report on numerical tests are given
Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems
Coupled problems with various combinations of multiple physics, scales, and
domains are found in numerous areas of science and engineering. A key challenge
in the formulation and implementation of corresponding coupled numerical models
is to facilitate the communication of information across physics, scale, and
domain interfaces, as well as between the iterations of solvers used for
response computations. In a probabilistic context, any information that is to
be communicated between subproblems or iterations should be characterized by an
appropriate probabilistic representation. Although the number of sources of
uncertainty can be expected to be large in most coupled problems, our
contention is that exchanged probabilistic information often resides in a
considerably lower dimensional space than the sources themselves. In this work,
we thus use a dimension-reduction technique for obtaining the representation of
the exchanged information. The main subject of this work is the investigation
of a measure-transformation technique that allows implementations to exploit
this dimension reduction to achieve computational gains. The effectiveness of
the proposed dimension-reduction and measure-transformation methodology is
demonstrated through a multiphysics problem relevant to nuclear engineering
A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn-Hilliard-Navier-Stokes system
This paper is concerned with the development and implementation of an
adaptive solution algorithm for the optimal control of a time-discrete
Cahn-Hilliard-Navier-Stokes system with variable densities. The free energy
density associated to the Cahn-Hilliard system incorporates the
double-obstacle potential which yields an optimal control problem for a
family of coupled systems in each time instant of a variational inequality of
fourth order and the Navier-Stokes equation. A dual-weighted residual
approach for goal-oriented adaptive finite elements is presented which is
based on the concept of C-stationarity. The overall error representation
depends on primal residuals weighted by approximate dual quantities and vice
versa as well as various complementarity mismatch errors. Details on the
numerical realization of the adaptive concept and a report on numerical tests
are given
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